Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

644 Chapter 19 Probability and Statistics in Engineering

students, then we might be able to use the probability distribution for this class to predict how

students might do on a similar test next year. Often, it is difficult to define what we mean by

a typical class or a typical test. However, if we had a lot more students take this test and incor-

porate their scores into our analysis, we might be able to use the results of this experiment to

predict the outcomes of a similar test to be given later. As the number of students taking the

test increases (leading to more scores), the line connecting the midpoint of scores shown in

Figure 19.4 becomes smoother and approaches a bell-shaped curve. We use the next example

to further explain this concept.

Example 19.4 In order to improve the production time, the supervisor of assembly lines in a manufacturing

setting of computers has studied the time that it takes to assemble certain parts of a computer

at various stations. She measures the time that it takes to assemble a specific part by 100 people

at different shifts and on different days. The record of her study is organized and shown in

Table 19.10.

TABLE 19.10 Data Pertaining to Example 19.4

Time That It

Takes a Person

to Assemble the

Part (minutes) Frequency Probability

5 5 0.05

6 8 0.08

7 11 0.11

8 15 0.15

9 17 0.17

10 14 0.14

11 13 0.13

12 8 0.08

13 6 0.06

14 3 0.03

Based on data provided, we have calculated the probabilities corresponding to the time

intervals that people took to assemble the parts. The probability distribution for

Example 19.4 is shown in Table 19.10 and Figure 19.5. Again, note that the sum of proba-

bilities is equal to 1. Also note that if we were to connect the midpoints of time results

(as shown in Figure 19.5), we would have a curve that approximates a bell shape. As the

number of data points increases and the intervals decrease, the probability-distribution curve

becomes smoother. A probability distribution that has a bell-shaped curve is called anormal

distribution. The probability distribution for many engineering experiments is approximated

by a normal distribution.

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